American public school districts are rethinking how to teach reading to the youngest children. They have thrown out old lesson plans, retrained teachers and bought new reading programs.

But the national movement to rethink reading has largely left out a generation of older students who are behind in literacy — and who will not recover without extra help.

In New York, where the Education Department is in the midst of a high-stakes elementary reading overhaul, the scale of the reading problems for these students is striking.

More than 60 percent of the city’s Black and Latino middle schoolers were not proficient in reading on this year’s state exams. In the Bronx, over 37 percent of middle-school boys scored in the bottom level, meaning they did not demonstrate even partial mastery of skills expected for their age.

At the city’s lowest-income high schools, it is not uncommon for a quarter of incoming freshmen to test at or below a third-grade reading level.

And yet New York, like many districts around the country, has no comprehensive plan to tackle the issue.